Endwall aerodynamic losses from turbine components within gas turbine engines

Endwall aerodynamic losses from turbine components within gas turbine engines Q2 Q1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42[.]

10:0:1465=WUnicodeDec222011ị 6ỵ model JPPR : 124 Prod:Type:FTP pp:0214col:fig::NILị ED: PAGN: SCAN: Propulsion and Power Research ]]]];](]):]]]–]]] 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 HOSTED BY http://ppr.buaa.edu.cn/ Propulsion and Power Research www.sciencedirect.com Q2 Endwall aerodynamic losses from turbine components within gas turbine engines Q1 Phil Ligrania,n, Geoffrey Pottsb, Arshia Fatemic a Propulsion Research Center, Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, 5000 Technology Drive, Olin B King Technology Hall S236, Huntsville, Alabama 35899, USA b Aero/Thermal & Heat Transfer, Solar Turbines, Inc., 2200 Pacific Highway, P O Box 85376, Mail Zone C-9, San Diego, California 92186-5376, USA c Robert Bosch GmbH (CR/ARF2), Robert Bosch Central Research 130-1, Robert Bosch Campus 1, Renningen 71272, Germany Received August 2016; accepted 30 November 2016 KEYWORDS Aerodynamic losses; Gas turbine engines; Turbine components; Airfoil/endwall interactions; Secondary flows; Vorticity; Endwall contouring Abstract A survey of research on aerodynamic loss investigations for turbine components of gas turbine engines is presented Experimental and numerically predicted results are presented from investigations undertaken over the past 65 plus years Of particular interest are losses from the development of secondary flows from airfoil/endwall interactions The most important of the airfoil/endwall secondary flows are passage vortices, counter vortices, and corner vortices The structure and development of these secondary flows are described as they affect aerodynamic performance within and downstream of turbine passage flows in compressible, high speed flows with either subsonic or transonic Mach number distributions, as well as within low-speed, incompressible flows Also discussed are methods of endwall contouring, and its consequences in regard to airfoil/endwall secondary flows & 2017 National Laboratory for Aeronautics and Astronautics Production and hosting by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Introduction n Corresponding author E-mail addresses: pml0006@uah.edu (Phil Ligrani), Potts_Geoffrey_A@solarturbines.com (Geoffrey Potts), Arshia.Fatemi@de.bosch.com (Arshia Fatemi) Peer review under responsibility of National Laboratory for Aeronautics and Astronautics, China Losses in a gas turbine engine are typically divided into profile losses, tip clearance losses, and end-wall losses Profile losses are caused by the blade or vane “profile” and are generated on the airfoil surface due to the growth of boundary layers Tip leakage losses mostly occur in rotors and are due to the pressure difference that is formed over http://dx.doi.org/10.1016/j.jppr.2017.01.006 2212-540X & 2017 National Laboratory for Aeronautics and Astronautics Production and hosting by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 2 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Phil Ligrani et al Nomenclature c cx Cx Cp Cωs ELC h h htc IAL k Me Me,ideal Me1 _ m p Po Poc poe Poe Poe,m Poe1 poi Poi Poi,m Poi1 pse Pse Pse,m poe,A pse,A PS qe qe,m R s se si SS True chord length of airfoil Axial chord length of airfoil Axial chord length of airfoil Local total pressure loss coefficient, ( Poi  Poe)/ Poi Streamwise vorticity coefficient Energy loss coefficient Enthalpy Flow passage height Heat transfer coefficient Integrated aerodynamic losses Ratio of specific heats Exit local Mach number downstream of the airfoil Ideal isentropic exit local Mach number downstream of the airfoil Exit freestream Mach number downstream of the airfoil Mass flow rate Airfoil passage effective pitch Stagnation pressure Injectant stagnation pressure Exit local stagnation pressure Exit local stagnation pressure Mass-averaged exit stagnation pressure Exit freestream stagnation pressure Inlet local stagnation pressure Inlet local stagnation pressure Mass-averaged inlet stagnation pressure Inlet freestream stagnation pressure Exit local static pressure Exit local static pressure Mass-averaged exit static pressure Area-averaged exit stagnation pressure Area-averaged exit static pressure Pressure side Exit local dynamic pressure Mass-averaged exit dynamic pressure Gas constant Span spacing between adjacent airfoils Local exit entropy Local inlet entropy Suction side the blade tip between the pressure and suction sides of the blade The third major type of loss, known as end-wall loss or secondary flow loss, is due to viscous effects from the presence of the end-wall and the interaction of the end-wall boundary layers the airfoils The primary flow that is created by blades and vanes is diverted due to viscous effects and gives rise to secondary flows The existence of end-walls in an axial flow turbomachine is a large contributor to the complexity of three-dimensional flow downstream blades and vanes For a turbine blade row with low aspect ratio, secondary flow losses can attribute to as high as 30%–50% of the total aerodynamic loss in a single blade row [14] As a result, investigations have been working for many years to better understand such secondary flows Te Tu u u1 W Wc Wc,ideal We We,ideal x X y Y YA YP YP YS z Exit absolute temperature Test section inlet longitudinal turbulence intensity level Local streamwise velocity Local streamwise freestream velocity Local relative velocity Local injectant relative velocity Local injectant ideal isentropic relative velocity Local exit relative velocity Local exit ideal isentropic relative velocity Streamwise coordinate Streamwise coordinate Spanwise coordinate Spanwise coordinate Area-averaged loss coefficient Second-law loss coefficient Mass-averaged second-law loss coefficient Entropy rise coefficient Normal coordinate measured from endwall surface Greek symbols ρ ρ1 Ω ξ ξth ψn Local static density Freestream static density Omega total pressure loss coefficient Primary loss coefficient Thermodynamic loss coefficient Spanwise-normal plane location designation, n¼ 1, 2, 3, 4, or Subscripts A c i e m o s ideal Area-averaged Injectant or film coolant value at exit planes of film cooling holes Inlet of test section Exit of test section Mass-averaged Total or stagnation Static Local freestream value Ideal isentropic value Early past investigations In the early 1950s, flow visualization techniques were employed by Herzig et al [1] that directly identified the existence of vortices in cascade passages Even before this time, other experimental and theoretical studies attempted to give a qualitative understanding of secondary flow behavior and to provide meaningful approximations of loss calculations (Herzig et al [1]; Carter [2]; Squire and Winter [3]) In 1955, Hawthorne [4] introduced the secondary flow vortex system shown in Fig In this model, Hawthorne suggests that flow passing through a cascade may be divided into three parts The first is a distributed secondary circulation that is the result of a distortion of vortex filaments carried Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Endwall aerodynamic losses from turbine components within gas turbine engines 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Fig Vortex model proposed by Hawthorne [4] Fig Vortex model proposed by Ö ngören [10] Fig Secondary flow vortex model proposed by Langston [8] with the stream and arises in flow around bends and between cascade passages The second part is a trailing shed vortex due to the change of circulation about the airfoil in the spanwise direction The third component is trailing filament vortices, which arise due to the vortex filament on the convex surface of the blade moving ahead of that on the concave surface, thus causing it to stretch Hawthorne also noted that the stretched filaments contribute to a vorticity of the same sign as the trailing shed circulation, and that, together, they form a trailing vortex sheet which separates the upper and lower parts of the flow from each other It was not until 1966 that Klein [5] identified the existence of a stagnation point vortex – essentially a point upstream the leading edge of the airfoil in which the flow separated into a horseshoe vortex Other than Klein's discovery, significant advancements in the study of secondary flow phenomena were relatively small in the 1960s Related endwall loss studies carried out before 1970 are described by Dunham [6] One of the earliest comprehensive experimental investigations into the behavior of endwall flow was performed by Langston et al [7] in 1976 The result of their investigation is depicted by the model in Fig which shows the three-dimensional separation of a boundary layer entering a linear turbine cascade (Langston [8]) Langston's model was derived from a test conducted in a large-scale, low-speed wind tunnel that showed that the inlet boundary layer separates at the endwall of the cascade As the flow enters the cascade and encounters a solid body (in this case, a turbine blade) the effects of longitudinal and vertical pressure gradients, combined with the momentum deficit in the boundary layer, cause the flow to separate and form one or more vortices (Ballio et al [9]) This is similar to the “stagnation point vortex” proposed by Klein [5] nearly a decade earlier This point of flow separation, known as the saddle point, occurs at the location of highest static pressure on the endwall as depicted in Fig 4a as point A (Langston [8]) At this point, a horseshoe vortex comprised of two vortex “legs” is formed and a majority of the fluid from the inlet boundary is contained within these legs In the cascade, the first horseshoe vortex leg, known as the pressure leg, is pulled into the passage between two blades This vortex is fed through the passage and occurs near the suction surface due to transverse fluid motion from the pressure to the suction surface along the endwall Because it is fed through the passage, this vortex is typically labeled as the passage vortex or secondary vortex The second vortex leg, known as the suction leg, is pulled into an adjacent cascade passage with the opposite sense of rotation of the passage vortex This second vortex is called the counter vortex Such behavior is illustrated in Fig from Ö ngören [10] Several important advances are depicted by this drawing, relative to earlier concepts First, the counter vortex is shown to be displaced away from the Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 4 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Phil Ligrani et al Fig (a) Static pressure contours measured by Langston [8], and (b) velocity field proposed by Hah [11] Fig Model proposed by Sieverding and Van den Bosch [13] that show counter vortex rotation about the passage vortex endwall by secondary flows associated with the passage vortex In addition, a separate corner vortex forms near the airfoil/endwall junction, which is located beneath the passage vortex Note that attachment lines, separation lines, and saddle points are also denoted within Fig Additional details regarding such flow structural characteristics are provided by Hah [11] Of particular importance are separation and reattachment lines, which are identified by predicted velocity vectors given by Hah [11] and by Lakshiminarayana [12] in Fig 4(b) Here, the separation lines s1 and s2 correspond to the paths of the passage vortex (s1) and counter vortex (s2) The paths of each vortex are also apparent by examining the regions of low endwall static pressure in Fig 4(a) from Langston [8] In the 1980s, Sieverding and Van den Bosch [13] used a colored smoke wire technique to visualize the entire stream surface through a cascade, and showed that it is possible Fig Secondary flow vortex model proposed by Sharma and Butler [14] that the counter vortex rotates about the axis of the passage vortex as shown in Fig Sharma and Butler [14] used these findings along with others (Langston et al [7]; Graziani et al [15]; Sieverding [16]; Kopper et al [17]; Sharma et al [18]) to build a new secondary flow model, which is depicted in Fig Sharma and Butler [14] show that neither the loss nor the streamwise voriticty attributable to the inlet boundary layer increase as the boundary layer passes through the cascade passage The inlet boundary layer entering the cascade does not, in fact, experience flow turning in the passage As such, this result is not consistent with secondary flow theories proposed by Hawthorne [4] and Langston [7] Sharma and Butler [14] show that the formation of the horseshoe vortex transforms incoming Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Endwall aerodynamic losses from turbine components within gas turbine engines 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Fig Secondary flow vortex model proposed by Wang et al [20] normal vorticity to streamwise vorticity independent of the flow turning These findings imply that inlet boundary losses are not dependent on the amount of turning from the airfoil, and that the inlet boundary layer actually interacts with the airfoil leading edge as it enters the cascade In 1988, Goldstein and Spores [19] presented a revised secondary flow vortex model that proposes that the suction leg of the horseshoe vortex stays above the passage vortex and travels with it Wang et al [20] support this model by presenting multiple smoke-wire flow visualization observations which track the vortices, and compare them to local mass transfer measurements An example of their results is shown in Fig With such data, Wang et al [20] demonstrate the existence of a wall vortex near the suction surface that is induced by the passage vortex The interaction of the endwall with the inlet boundary layer, the inlet turbulence, the airfoil surface roughness, the airfoil leading edge radius, pitch, and flow speed all play critical roles in the formation and interaction of secondary flow vortices As discussed, new vortex models are consistently arising as cutting-edge research is performed While secondary flow theory shows significant advancement since the originally proposed models from the 1950s, there is still much work to be done, especially in understanding of flows at transonic speeds As such, a summary of the state of knowledge of turbine cascade secondary flow theory, from these different investigations undertaken up to 1997, is as follows (i) A horseshoe vortex is formed at a saddle point upstream of the leading edge of an airfoil This horseshoe vortex consists of two legs, the pressure leg and suction leg The pressure leg travels across the blade row passage toward the suction surface of the adjacent blade and becomes a major portion of what is called the passage vortex This phenomenon occurs due to transverse fluid motion from the pressure to the suction surface along the endwall The suction leg moves into the passage with the opposite sense of rotation than that of the passage vortex and merges with the passage vortex from the adjacent blade at approximately 25% of the surface distance from the leading edge The overall sense of direction of the passage vortex is that it is moving from the pressure side of the first airfoil towards the trailing edge of the suction side of the second airfoil (ii) As demonstrated by Wang et al [20], the suction leg of the horseshoe vortex moves above the passage vortex as the pressure and suction legs merge Sieverding and Van den Bosch [13] demonstrate that the counter vortex wraps around the passage vortex (iii) A wall vortex near the suction surface is induced by the passage vortex and starts near the merging point of the suction side and pressure side legs Quantitative aerodynamic loss characterization Quantifying aerodynamic loss is challenging due to the number of variables that influence local and overall mixing losses Highlighted here are non-dimensional loss coefficients that are key performance metrics, and are also employed for turbomachinery analysis 3.1 Primary loss coefficient and thermodynamic loss coefficient According to Raffel and Kost [21], Kost and Holmes [22], Mee et al [23], and Drost and Bolcs [24], a primary loss coefficient is given by
 hoe  hse ẳ 1 1ị hoi  hse;ideal which is also equivalent to the following " # " ðk  1ị=k #  Pse =Poe W 2e ẳ 1 ẳ 1  k  1ị=k ; W 2e;ideal ð1  Pse =Poi ð2Þ where W is the local relative velocity A thermodynamic loss coefficient is then employed to account for the different energy input of coolant flow relative to the mainstream flow (Raffel and Kost [21])    _ c =m _ W 2e 1ỵ m 5: th ẳ  4 3ị   W 2e;ideal ỵ m_ c =m_ W 2c;ideal Eq (3) can also be expressed using an equation given by
h  i    _ c =m _1 1ỵ m th ẳ   Pse =Poe Þðk  1Þ=k hoc   ðk  1Þ=k  =  Pse =Poi hoi      ðk  1Þ=k _ 1  ðPse =Poc ị _ c =m ỵ m 4ị hoc Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 6 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Phil Ligrani et al determined With mass averaging, the ðPoi  Poe Þ quantity within the total loss coefficient Ω is multiplied by local mass flow rate The result is normalized by overall mass flow rate multiplied by ðPoi  Pse Þ This gives the massweighted stagnation pressure loss, relative to overall ideal dynamic pressure for the equivalent of one blade passage Ames et al [27], Johnson et al [29], and Fiala et al [31] also consider local and cross-passage mass-averaged magnitudes of turning angle, which is defined as the outlet flow angle measured relative to the inlet axial direction 3.4 Area-averaged loss coefficients Fig Comparison of area-averaged loss coefficients with values from Boyle and Senyitko [32], and Boyle et al [33], for smooth, cambered vanes from Zhang et al [35] 3.2 Entropy rise coefficient According to Denton [25], an entropy rise coefficient can also be utilized to characterize turbomachinery stage losses Such a coefcient is dened using YS ẳ ẵT e se  si ị  ẵhoe  hse  5ị For small losses in incompressible flow, this is then equivalent to a stagnation pressure loss coefficient YP ¼ ðPoi  Poe Þ ðPoi  Pse Þ ð6Þ which is, thus, also a second-law loss coefficient Such coefficients are useful because they allow appropriate comparison to be made between difference airfoils, with different film cooling arrangements, at different flow velocities 3.3 Omega aerodynamic loss coefficients Within investigations which generally involve low-speed turbine cascades (Ames and Plesniak [26]; Ames et al [27]; Jaswal et al [28]; Johnson et al [29]; Erickson et al [30]; Fiala et al [31]), a total pressure loss coefcient ẳ Poi  Poe ị=Poi  Pse ị is employed, which is equivalent to the Y P quantity given in by Eq (6) Within this definition, each term is generally determined locally at a particular spatial location Here, the stagnation pressure loss is normalized by idealized dynamic pressure, which is equivalent to the sum of the stagnation pressure loss and the local exit dynamic pressure In the investigations of Ames et al [27] and Johnson et al [29], cross-passage mass-averaged and full exit massaveraged magnitudes of aerodynamic loss (determined by integrating distributions of loss coefficient Ω) are also Boyle and Senyitko [32] and Boyle et al [33] employ an area averaged loss coefficient, Y A , in their analysis, which is defined using an equation of the form poi  poe;A YA ẳ : 7ị poi  pse;A The form of (7) is similar to the form of (6), except, here, poe;A and pse;A are area averaged exit total pressure and static pressure, respectively These are determined using equations, respectively, given by  Z p=2 dy poe;A ¼ poe ; p  p=2  Z p=2 dy pse;A ¼ pse : ð8Þ p  p=2 Examples of area-averaged loss coefficient Y A data are presented in Fig Here, Y A data from Boyle and Senyitko [32] are given which are based on measurements made 0.35 of an axial chord length downstream of their vane trailing edge Vanes are employed with 5.18 cm axial chord length and 751 flow turning angle The prediction results from Boyle et al [34] represent data from vanes with 4.445 cm axial chord length and approximately 801 flow turning angle in their numerical prediction Fig also includes results from Zhang et al [35] measured downstream of a smooth cambered vane at two different exit Mach numbers for a location 0.25cx downstream of the vane 3.5 Local total pressure loss coefficient and integrated aerodynamic loss C p is the normalized inlet total pressure minus exit total pressure (Zhang et al [35–37]; Jackson et al [38]; Chappell et al [39]; Zhang and Ligrani [40–43]), which is expressed using an equation of the form  Poi  Poe Poe Cp ẳ ẳ 1 : 9ị Poi Poi With this approach, the local stagnation pressure loss is normalized by a quantity which does not vary with cascade exit location Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Endwall aerodynamic losses from turbine components within gas turbine engines 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Zhang et al [35–37], Jackson et al [38], Chappell et al [39], and Zhang and Ligrani [40–43] employ integrated aerodynamic loss IAL to quantify aerodynamic losses in turbine components Dimensional magnitudes of Integrated Aerodynamic Loss, IAL, are determined by integrating profiles of ðPoi  Poe Þ with respect to y in the transverse flow direction across the wake for one single vane spacing, from  p=2top=2(Jackson et al [38]) In equation form, IAL is thus given by Z p=2 IAL ¼ ðPoi  Poe Þdy:  p=2 Here, IAL magnitudes are determined from measured distributions of the local total pressure loss coefficient, C p , which are measured downstream of the airfoil Consequently, IAL magnitudes represent mixing losses which have accumulated through the wake and airfoil boundary layers (Jackson et al., 2000) These forms for IAL and C p are employed because they are directly related to local entropy change and to local entropy creation When normalized using either Poi p or ðPoi  Pse Þp, IAL magnitudes can then be compared to data sets obtained at different velocities and with different airfoil configurations 3.6 Mass-averaged loss coefficients Kind et al [44] employ a mass averaged loss coefficient, Yp in their turbine cascade investigation, which is defined using Poi  Poe;m Yp ẳ 10ị qe;m where Poe,m and qe,m are mass-averaged exit total pressure, and mass-averaged dynamic pressure, respectively These two parameters are defined with equations that are given by R p=2  p=2 uPoe dy 11ị Poe;m ẳ u1 p and qe;m ¼ R p=2  p=2 ρuqe dy ρ1 u1 p ð12Þ respectively 3.7 Energy loss coefficient According to Taremi et al [45], an energy loss coefficient is given by   k  1=k ln Poi;m =Poe;m ELC ẳ 13ị  1   1 ỵ k  1ị=2 M 2e;ideal This parameter is a modified version of the entropy rise coefficient given by Eq (5) from Denton [24] Within Eq (13), Poi,m and Poe,m are generally determined as mass-averaged values, and the Mach number Me,ideal is an isentropic outlet value In addition, local ELC values are often presented as they are weighted by local mass flux (Taremi et al [45]) Recent investigations of aerodynamic loss due to secondary flow phenomena Overall, the most important parameters which affect the initiation and development of secondary flows within turbine cascade passages include the airfoil and endwall configuration and geometry Here, the most influential characteristics are aspect ratio, airfoil loading, and airfoil turning Note that airfoil loading is tied to blade spacing and pitch-to-span ratio Corner fillets and endwall contouring, if included, can also have important effects on associated development of vortex and secondary flow structures Other key influential parameters are cascade flow inlet characteristics, including inlet boundary layer characteristics (especially boundary layer thickness) The presence of swirl from the upstream combustion chamber is also important According Lin et al [46], the flow angle of swirl can be constant from endwall to endwall, or can vary in a linear fashion from one endwall to another The former situation is generally associated with silo-type combustors, whereas the latter arrangement simulates canister-type combustors with fuel/air swirlers Other recent investigations which consider secondary flow phenomena which affect turbine blade aerodynamic losses are now discussed Included are the influences of a variety of physical effects According to Langston [47], turbine airfoil passage secondary flows, such as the horseshoe, passage, counter, and corner vortices, have dramatic and detrimental effects on the performance, reliability, and efficiency of gas turbine engines In 1992, Gregory-Smith and Cleak [48] investigate the influence of inlet turbulence on losses across turbine cascades High inlet turbulence levels are obtained using a turbulence grid upstream of the cascade Using a five-hole probe and two x-wire probes to obtain velocity data, total pressure data, and Reynolds normal and shear stresses, Gregory-Smith and Cleak [48] show that inlet turbulence levels as high as percent have little effect on the secondary loss or kinetic energy of secondary flow Also given is a detailed insight into the contribution of Reynolds stress to loss generation In 1987, Hoheisel et al [49] consider the influences of inlet turbulence across turbine cascades Hoheisel et al also investigate the effects of blade boundary layers In 1997, Ames and Plesniak [26] demonstrate the important connections between wake grown and level of freestream turbulence In 1999, Duden et al [50] study the effects of endwall contouring and endwall pressure distribution and their influence on secondary flow Findings showed an approx 25 percent decrease in secondary loss, but the reduction was mostly counteracted by increased profile losses and inlet losses due to blockage In 2010, Tsujita Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Phil Ligrani et al Fig Computed heat transfer coefficients on airfoil and end wall surfaces for the C2 configurations from Lin et al [46] Results for a flat endwall are compared to contour endwall results, with suction side and pressure side vane results, also given for a contoured endwall Data are obtained with zero swirl and Yamamoto [51] describe the effects of inlet boundary layer thickness and incidence angle on secondary flow structures in a turbine cascade They show that there is minimal influence from the inlet boundary layer thickness on the formation of the horseshoe vortex and passage vortex In 2012, Lei et al [52] examines the physical mechanism of the streamwise vortex interaction with secondary flow with the use of a vortex generator Perdichizzi [53] gives an extensive overview on the effect of Mach number on secondary flow development With experiments ranging from Mach number of 0.2–1.55, it is shown that the importance of secondary losses diminishes when compared to profile losses as the Mach number rises Also described is the movement of secondary vortices as Mach number varies Mee et al [23] show that boundary layers, shock waves, and wakes mixing all contribute to overall losses in relative amounts which depend upon the Mach number for a study whose results are presented in 1992 In addition, most of the mixing losses are generated immediately downstream of the trailing edges of blades where gradients in properties across the wake are largest Izsak and Chiang [54] present experimental data and numerical predictions which account for turbulence, transition, as well as transonic expansion fans Michelassi et al [55] test turbulence and transition models, which include the effects of separation bubbles, for a cascade flow with shock-boundary layer interactions McVetta et al [56] investigates the effect of blade incidence angle, showing a strong correlation of blade-row loss levels with Zweifel coefficient, along with the finding that the Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Endwall aerodynamic losses from turbine components within gas turbine engines 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Fig 10 Streamwise vorticity coefficients superimposed with contour lines of mass-weighted energy loss coefficient (Taremi et al [45]), which show weakening of passage and counter vortex due to endwall contouring, as investigated by Taremi et al [45] correlation breaks down at extreme negative incidence Jouybari et al [57] give an overview of many modern pressure loss models and compares them to experimental results Berrino et al [58] compares aerodynamic performance of three turbine cascades Evaluation of blade performance in terms of secondary losses is performed by examining the effects of loading distribution on the airfoils Endwall contouring and alterations of secondary flow phenomena Early investigations of the development and consequences of turbine passage endwall contouring are described by Deich et al [59], Ewen at al [60]., Duden et al [50], Dossena et al [61] and Burd and Simon [62] More recently, Shih et al [63] examine flow within a nozzle guide vane passage with one flat endwall and with one contoured endwall Two different contour arrangements are considered: one with all contouring upstream of the airfoils, and one with contouring starting upstream of the airfoils and then continuing through the airfoil passages According to the investigators, the intensities of secondary flows are reduced with the second arrangement Another investigation by Lin and Shih [64] addresses effects of inlet Mach number on the same two contoured endwall arrangements Reduced secondary flows, reduced surface heat transfer coefficients, and lower losses in stagnation pressure are again present with the second arrangement A later investigation by Shih and Lin [65] considers methods to reduce aerodynamic losses, reduce surface heat transfer, and control secondary flow structure, using inlet swirl and leading-edge airfoil fillets Lin et al [46] investigate effects of inlet swirl angle on flow and heat transfer within a nozzle guide vane passage with one contoured endwall An example of computed heat transfer coefficients on airfoil and end wall surfaces for the C2 configuration is shown in Fig These particular data are obtained with zero swirl angle Within this figure, results for a flat endwall are compared to contour endwall results Suction side and pressure side vane results are also given the for a contoured endwall arrangement From these results, it is evident that local surface heat transfer coefficients on the contoured endwall are substantially less than on the flat endwall Here, the overall heat transfer rate on the contoured endwall is 2865.4 W, compared to Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 10 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Phil Ligrani et al Fig 11 Heat transfer coefficient distribution for an ice-contoured endwall (left), and distribution of heat transfer coefficient ratio of contoured to flat endwall (right), for a chord Reynolds number of 49,900, from Winkler [68] 3071.2 W on the flat endwall These reductions are a result of diminished secondary flows caused by the contouring Also evident are relatively high surface heat transfer coefficients on the airfoil suction surface near the bladeto-blade throat region Other recent endwall contouring studies are described by Moser et al [66,67] These investigators develop shroud contour designs which are defined by an axisymmetric shroud contour, and particular stagger angle and blade contour distributions With such arrangements, the passage vortex is degraded and dislocated relative to the endwall As a result, efficiency and power output of the stage are increased at full load and subcritical pressure ratios Taremi et al [45] address the effects of endwall contouring on secondary flow losses Detailed experimental results, including total pressure losses, streamwise vorticity, and secondary kinetic energy, are provided Taremi et al show that the implementation of endwall contouring results in less intense vortical structures and a reduction in secondary kinetic energy Fig 10 shows the weakening of the passage and counter vortex with the application of endwall contouring Presented in this figure are streamwise vorticity coefficients superimposed with contour lines of mass-weighted energy loss coefficient (Taremi et al [45]) Results are shown for two linear cascade configurations: SL1F and SL2F with flat endwalls, and SL1C and SL2C with contoured endwalls Here, the SL2F and SL2C configurations are more highly loaded, compared to the SL1F and SL1C arrangements The higher loading in SL2 is associated with the larger blade spacing and larger pitch-tospan ratio Based on the right-handed Cartesian coordinate system employed, the passage vortex has positive vorticity, and the counter and corner vortices have negative vorticity Here, the SL1F and SL1C results show that the locations and extents of the vortical structures are not changed noticeably by contouring However, contouring has slightly decreased the intensities of the passage vortex and the counter vortex The more highly loaded SL2 cascade displays stronger secondary flow structures than SL1 With SL2, use of endwall contouring decreases the sizes and strengths of the passage and counter vortices Such behavior is illustrated by only one distinct loss core for the SL2C arrangement, compared to two loss cores with the SL2F configuration Another endwall contouring example is provided from Winkler [68] Within this investigation, the endwall contour shape is obtained using an IFM or ice formation method, which relies upon natural processes wherein energy dissipation and entropy production are minimized Fig 11 shows heat transfer coefficient distributions for an icecontoured endwall, as well as the distribution of the ratio of ice-contoured heat transfer coefficient to flat endwall heat transfer coefficient Fig 12 then gives endwall heat transfer coefficient distributions and near-endwall flow field characteristics for baseline and ice-contoured endwalls for three flow cross-sectional planes All of these data are provided for a turbine flow passage associated with a vane chord Reynolds number of 49,900 Note that ice-contouring associated with these results s imposed only within the vane blades passages, with endwall transition regions just upstream and just downstream The ratio data given in Fig 11 shows that contouring significantly alters the endwall heat transfer coefficient distribution, with local values which are both lower and higher compared to baseline results Such behavior is illustrated by ratios which are above unity indicating increased heat transfer for the ice contour, and by ratios which are below unity, where the ice-contoured endwall values are lower than baseline values Such changes are strongly linked to the altered flow field due to the contouring As a result, with the ice-contoured endwall, the passage vortex does not advect as far downstream as for the baseline, since the contouring breaks up the vortex system at the trailing edge by diffusing it This results in an upwards shift of the vortex system away from the endwall and less vortex spread as it advects downstream (Winkler [68]) Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Endwall aerodynamic losses from turbine components within gas turbine engines 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 11 Fig 12 Distributions of heat transfer coefficient and near endwall flow field for baseline and ice-contoured endwall arrangements for flow cross sections Ψ3, Ψ4, and Ψ5, for a chord Reynolds number of 49,900, from Winkler [68] Fig 12 shows endwall heat transfer and z-velocities, plus path lines, for the three cross-sections Ψ3, Ψ4, and Ψ5 in the outflow region downstream of the vane cascade, again for the ice-contoured endwall and the baseline endwall The crosssections are perpendicular to the outflow direction and located directly at the trailing edge, as well as at distances of and axial chord lengths downstream of the trailing edge For the flat endwall baseline, the heat transfer distributions exhibit a distinct trend at all cross-sections, with a local maximum in the pressure side region (0oψo0.5) and a local minimum in the suction side region (0.5oψo1) Here, the maximum surface heat transfer occurs at the position where the vortex induces the highest velocities which are directed towards the endwall These are present near the trailing edge of the vane cascade Minimum heat transfer occurs near locations with the highest upwash direction velocities For the contoured endwall, both heat transfer and the near-endwall flow field differ from the baseline For the first cross-section (Ψ ), the contoured endwall also exhibits local maximum and minimum values of surface heat transfer coefficient This maximum is located at about the same position as for the baseline, but takes a slightly higher value, since the contoured endwall produces higher downwards velocities at this position Because of vortex breakup and diffusion in the downstream portions of the cascade, contoured endwall heat transfer coefficients are more uniform for cross sections Ψ4, and Ψ5, compared to baseline results No distinct maximum and minimum values are present, since velocity distributions provide no substantial evidence of vortices at these locations [68] Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 12 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Phil Ligrani et al Summary and conclusions References An overview on the development of secondary flow models and a survey of recent research on aerodynamic loss investigations for turbine endwalls are presented The influences of secondary flow phenomena are described as they affect the aerodynamic performance of turbine cascade passage flows Of interest are losses from the development of secondary flows from airfoil/endwall interactions Secondary flow descriptions and models proposed by a variety of investigators are discussed, including implications in quantifying local and overall aerodynamic losses Also considered are methods of endwall contouring, and the resulting consequences in regard to alteration of airfoil/ endwall secondary flows and surface heat transfer coefficient distributions Overall, results from several sources show that boundary layers, shock waves, and wakes mixing all contribute to overall losses in relative amounts which depend upon the Mach number In addition, most of the mixing losses are generated immediately downstream of the trailing edges of blades where gradients in properties across the wake are largest Important losses also result from passage vortices, counter vortices, and corner vortices which originate within the viscous flows which develop along endwalls The most important parameters which affect the initiation and development of such secondary flows within turbine cascade passages are airfoil and endwall configuration and geometry Here, the most influential characteristics are aspect ratio, airfoil loading, and airfoil turning Note that airfoil loading is tied to blade spacing and pitch-to-span ratio Corner fillets and endwall contouring, if included, can also have important effects on associated development of vortex and secondary flow structures Other key influential parameters are cascade flow inlet characteristics, including inlet boundary layer characteristics (especially boundary layer thickness) The presence of swirl from the upstream combustion chamber is also important Comparing results for a flat endwall to contour endwall results shows that local surface heat transfer coefficients on the 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Thesis), Institute of Aerospace Thermodynamics, University of Stuttgart, Stuttgart, Germany, 2016 Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 ... profile losses and inlet losses due to blockage In 2010, Tsujita Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, ... 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Endwall aerodynamic losses from turbine components within gas turbine engines 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27... from the Please cite this article as: Phil Ligrani, et al., Endwall aerodynamic losses from turbine components within gas turbine engines, Propulsion and Power Research (2017), http://dx.doi.org/10.1016/j.jppr.2017.01.006